A gas turbogroup with so-called sequential combustion has become known from EP 620 362. In this gas turbogroup, a first turbine is arranged downstream of a first combustion chamber, a second combustion chamber is arranged downstream of the first turbine, and a second turbine is arranged downstream of the second combustion chamber. In this case, the second combustion chamber is constructed as a so-called auto-ignition combustion chamber. The cooling of such a combustion chamber is described in EP 669 500. There, the combustion chamber wall is convectively cooled. The cooling air is introduced into the main flow of the gas turbogroup at the pressure level of the second combustion chamber. In relation to this, WO 03/038255 has described a gas turbogroup in which the second combustion chamber, or low-pressure combustion chamber, is cooled by air which is tapped in an intermediate stage of the compressor. That is to say, the air which is used for cooling the second combustion chamber is supplied at reduced pressure, wherein this pressure is adjusted to the pressure in the second combustion chamber and downstream of the second combustion chamber. In WO 03/038255, operating states of the gas turbogroup are described, in which the pressure build-up inside the compressor is shifted, and the intermediate tapping of cooling air at reduced pressure from the compressor can be problematical.